LEADER 04695nam 2200577Ia 450 001 9910962802103321 005 20251117074543.0 010 $a1-907343-66-0 010 $a1-904602-91-6 035 $a(CKB)2470000000002006 035 $a(EBL)3007749 035 $a(SSID)ssj0000421018 035 $a(PQKBManifestationID)11268405 035 $a(PQKBTitleCode)TC0000421018 035 $a(PQKBWorkID)10393650 035 $a(PQKB)10487876 035 $a(MiAaPQ)EBC3007749 035 $a(Au-PeEL)EBL3007749 035 $a(CaPaEBR)ebr10303283 035 $a(OCoLC)923619072 035 $a(BIP)15267911 035 $a(EXLCZ)992470000000002006 100 $a20071223d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to mathematical optimization $efrom linear programming to metaheuristics /$fXin-She Yang 210 $aCambridge, UK $cCambridge International Science Publishing$dc2008 215 $a1 online resource (160 p.) 300 $aDescription based upon print version of record. 311 08$a1-904602-82-7 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Preface""; ""1. Mathematical Optimization""; ""1.1 Optimization""; ""1.2 Optimality Criteria""; ""1.3 Computational Complexity""; ""1.4 NP-Complete Problems""; ""2. Norms and Hessian Matrices""; ""2.1 Vector and Matrix Norms""; ""2.2 Eigenvalues and Eigenvectors""; ""2.3 Spectral Radius of Matrices""; ""2.4 Hessian Matrix""; ""2.5 Convexity""; ""3. Root-Finding Algorithms""; ""3.1 Simple Iterations""; ""3.2 Bisection Method""; ""3.3 Newtona???s Method""; ""3.4 Iteration Methods""; ""4. System of Linear Equations""; ""4.1 Linear systems""; ""4.2 Gauss Elimination"" 327 $a""4.3 Gauss-Jordan Elimination""""4.4 LU Factorization""; ""4.5 Iteration Methods""; ""4.5.1 Jacobi Iteration Method""; ""4.5.2 Gauss-Seidel Iteration""; ""4.5.3 Relaxation Method""; ""4.6 Nonlinear Equation""; ""4.6.1 Simple Iterations""; ""4.6.2 Newton-Raphson Method""; ""5. Unconstrained Optimization""; ""5.1 Univariate Functions""; ""5.2 Multivariate Functions""; ""5.3 Gradient-Based Methods""; ""5.3.1 Newtona???s Method""; ""5.3.2 Steepest Descent Method""; ""5.4 Hooke-Jeeves Pattern Search""; ""6.Linear Mathematical Programming""; ""6.1 Linear Programming""; ""6.2 Simplex Method"" 327 $a""6.2.1 Basic Procedure""""6.2.2 Augmented Form""; ""6.2.3 A Case Study""; ""7. Nonlinear Optimization""; ""7.1 Penalty Method""; ""7.2 Lagrange Multipliers""; ""7.3 Kuhn-Tucker Conditions""; ""7.4 No Free Lunch Theorems""; ""8. Tabu Search""; ""8.1 Tabu Search""; ""8.2 Travelling Salesman Problem""; ""8.3 Tabu Search for TSP""; ""9. Ant Colony Optimization""; ""9.1 Behaviour of Ants""; ""9.2 Ant Colony Optimization""; ""9.3 Double Bridge Problem""; ""9.4 Multi-Peak Functions""; ""10. Particle Swarm Optimization""; ""10.1 Swarm Intelligence""; ""10.2 PSO algorithms""; ""10.3 Accelerated PSO"" 327 $a""10.4 Multimodal Functions""""10.5 Implementation""; ""10.6 Constraints""; ""11. Simulated Annealing""; ""11.1 Fundamental Concepts""; ""11.2 Choice of Parameters""; ""11.3 SA Algorithm""; ""11.4 Implementation""; ""12. Multiobjective Optimization""; ""12.1 Pareto Optimality""; ""12.2 Weighted Sum Method""; ""12.3 Utility Method""; ""12.4 Metaheuristic Search""; ""12.5 Other Algorithms""; ""Bibliography""; ""Index"" 330 $aThis book strives to provide a balanced coverage of efficient algorithms commonly used in solving mathematical optimization problems. It covers both the convectional algorithms and modern heuristic and metaheuristic methods. Topics include gradient-based algorithms such as Newton-Raphson method, steepest descent method, Hooke-Jeeves pattern search, Lagrange multipliers, linear programming, particle swarm optimization (PSO), simulated annealing (SA), and Tabu search. Multiobjective optimization including important concepts such as Pareto optimality and utility method is also described. Three Matlab and Octave programs so as to demonstrate how PSO and SA work are provided. An example of demonstrating how to modify these programs to solve multiobjective optimization problems using recursive method is discussed. 606 $aMathematical optimization 606 $aMathematical analysis 615 0$aMathematical optimization. 615 0$aMathematical analysis. 700 $aYang$b Xin-She$0781375 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910962802103321 996 $aIntroduction to mathematical optimization$94480894 997 $aUNINA